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The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation for further processing in the spike domain by Drosophila OSNs. In order to apply system identification techniques, we built a novel low-turbulence odor delivery system that allowed us to deliver airborne stimuli in a precise and reproducible fashion. The system provides a 1% tolerance in stimulus reproducibility and an exact control of odor concentration and concentration gradient on a millisecond time scale. Using this novel setup, we recorded and analyzed the in-vivo response of OSNs to a wide range of time-varying odor waveforms. We report for the first time that across trials the response of OR59b OSNs is very precise and reproducible. Further, we empirically show that the response of an OSN depends not only on the concentration, but also on the rate of change of the odor concentration. Moreover, we demonstrate that a two-dimensional (2D) Encoding Manifold in a concentration-concentration gradient space provides a quantitative description of the neuron's response. We then use the white noise system identification methodology to construct one-dimensional (1D) and two-dimensional (2D) Linear-Nonlinear-Poisson (LNP) cascade models of the sensory neuron for a fixed mean odor concentration and fixed contrast. We show that in terms of predicting the intensity rate of the spike train, the 2D LNP model performs on par with the 1D LNP model, with a root mean-square error (RMSE) increase of about 5 to 10%. Surprisingly, we find that for a fixed contrast of the white noise odor waveforms, the nonlinear block of each of the two models changes with the mean input concentration. The shape of the nonlinearities of both the 1D and the 2D LNP model appears to be, for a fixed mean of the odor waveform, independent of the stimulus contrast. This suggests that white noise system identification of Or59b OSNs only depends on the first moment of the odor concentration. Finally, by comparing the 2D Encoding Manifold and the 2D LNP model, we demonstrate that the OSN identification results depend on the particular type of the employed test odor waveforms. This suggests an adaptive neural encoding model for Or59b OSNs that changes its nonlinearity in response to the odor concentration waveforms.

Temporal experience of odor gradients is important in spatial orientation of animals. The fruit fly Drosophila melanogaster exhibits robust odor-guided behaviors in an odor gradient field. In order to investigate how early olfactory circuits process temporal variation of olfactory stimuli, we subjected flies to precisely defined odor concentration waveforms and examined spike patterns of olfactory sensory neurons (OSNs) and projection neurons (PNs). We found a significant temporal transformation between OSN and PN spike patterns, manifested by the PN output strongly signaling the OSN spike rate and its rate of change. A simple two-dimensional model admitting the OSN spike rate and its rate of change as inputs closely predicted the PN output. When cascaded with the rate-of-change encoding by OSNs, PNs primarily signal the acceleration and the rate of change of dynamic odor stimuli to higher brain centers, thereby enabling animals to reliably respond to the onsets of odor concentrations.DOI: http://dx.doi.org/10.7554/eLife.06651.001

We consider a formal model of stimulus encoding with a circuit consisting of a bank of filters and an ensemble of integrate-and-fire neurons. Such models arise in olfactory systems, vision, and hearing. We demonstrate that bandlimited stimuli can be faithfully represented with spike trains generated by the ensemble of neurons. We provide a stimulus reconstruction scheme based on the spike times of the ensemble of neurons and derive conditions for perfect recovery. The key result calls for the spike density of the neural population to be above the Nyquist rate. We also show that recovery is perfect if the number of neurons in the population is larger than a threshold value. Increasing the number of neurons to achieve a faithful representation of the sensory world is consistent with basic neurobiological thought. Finally we demonstrate that in general, the problem of faithful recovery of stimuli from the spike train of single neurons is ill posed. The stimulus can be recovered, however, from the information contained in the spike train of a population of neurons.

In noncooperative networks users make control decisions that optimize their own performance measure. Focusing on routing, we devise two methodologies for architecting noncooperative networks, that improve the overall network performance. These methodologies are motivated by problem settings arising in the provisioning and the run time phases of the network. For either phase, Nash equilibria characterize the operating point of the network. The goal of the provisioning phase is to allocate link capacities that lead to systemwide e cient Nash equilibria. In general, the solution of such design problems is counterintuitive, since adding link capacity might lead to a degradation of user performance. We show that, for systems of parallel links, such paradoxes cannot occur and the optimal solution coincides with the solution in the single-user case. We derive some extensions to general network topologies. During the run time phase, a manager controls the routing of part of the network ow. The manager is aware of the noncooperative behavior of the users and makes its routing decisions based on this information while aiming at improving the overall system performance. We obtain necessary and su cient conditions for enforcing an equilibrium that coincides with the global systemwide optimum, and indicate that these conditions are met in many cases of interest.

Over the past two decades, substantial amount of work has been conducted to characterize different odorant receptors, neuroanatomy and odorant response properties of the early olfactory system of Drosophila melanogaster. Yet many odorant receptors remain only partially characterized, and the odorant transduction process and the axon hillock spiking mechanism of the olfactory sensory neurons (OSNs) have yet to be fully determined. Identity and concentration, two key characteristics of the space of odorants, are encoded by the odorant transduction process. Detailed molecular models of the odorant transduction process are, however, scarce for fruit flies. To address these challenges we advance a comprehensive model of fruit fly OSNs as a cascade consisting of an odorant transduction process (OTP) and a biophysical spike generator (BSG). We model odorant identity and concentration using an odorant-receptor binding rate tensor, modulated by the odorant concentration profile, and an odorant-receptor dissociation rate tensor, and quantitatively describe the mechanics of the molecular ligand binding/ dissociation of the OTP. We model the BSG as a Connor-Stevens point neuron. The resulting spatio-temporal encoding model of the Drosophila antenna provides a theoretical foundation for understanding the neural code of both odorant identity and odorant concentration and advances the state-of-the-art in a number of ways. First, it quantifies on the molecular level the spatio-temporal level of complexity of the transformation taking place in the antennae. The concentration-dependent spatio-temporal code at the output of the antenna circuits determines the level of complexity of olfactory processing in the downstream neuropils, such as odorant recognition and olfactory associative learning. Second, the model is biologically validated using multiple electrophysiological recordings. Third, the model demonstrates that the currently available data for odorantreceptor responses only enable the estimation of the affinity of the odorant-receptor pairs. The odorant-dissociation rate is only available for a few odorant-receptor pairs. Finally, our model calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies.

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